Solve for x 2 cube root of x-3+15=10

$2 \sqrt[3]{x - 3 + 15} = 10$

To remove the radical on the left side of the equation, cube both sides of the equation.

${(2 \sqrt[3]{x - 3 + 15})}^{3} = 10^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 3 + 15}$ as ${(x - 3 + 15)}^{\frac{1}{3}}$ .

${(2 {(x - 3 + 15)}^{\frac{1}{3}})}^{3} = 10^{3}$

Simplify the left side.

Simplify ${(2 {(x - 3 + 15)}^{\frac{1}{3}})}^{3}$ .

Add $- 3$ and $15$ .

${(2 {(x + 12)}^{\frac{1}{3}})}^{3} = 10^{3}$

Apply the product rule to $2 {(x + 12)}^{\frac{1}{3}}$ .

$2^{3} {({(x + 12)}^{\frac{1}{3}})}^{3} = 10^{3}$

Raise $2$ to the power of $3$ .

$8 {({(x + 12)}^{\frac{1}{3}})}^{3} = 10^{3}$

Multiply the exponents in ${({(x + 12)}^{\frac{1}{3}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8 {(x + 12)}^{\frac{1}{3} \cdot 3} = 10^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$8 {(x + 12)}^{\frac{1}{3} \cdot 3} = 10^{3}$

Rewrite the expression.

$8 {(x + 12)}^{1} = 10^{3}$

Simplify.

$8 (x + 12) = 10^{3}$

Apply the distributive property.

$8 x + 8 \cdot 12 = 10^{3}$

Multiply $8$ by $12$ .

$8 x + 96 = 10^{3}$

Simplify the right side.

Raise $10$ to the power of $3$ .

$8 x + 96 = 1000$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $96$ from both sides of the equation.

$8 x = 1000 - 96$

Subtract $96$ from $1000$ .

$8 x = 904$

Divide each term in $8 x = 904$ by $8$ and simplify.

Divide each term in $8 x = 904$ by $8$ .

$\frac{8 x}{8} = \frac{904}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{904}{8}$

Divide $x$ by $1$ .

$x = \frac{904}{8}$

Simplify the right side.

Divide $904$ by $8$ .

$x = 113$

Solve for x 2 cube root of x-3+15=10

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